Invisible defects in complex crystals

• We show the existence of invisible localized defects in complex crystals.
• They turn out to be fully invisible to Bloch waves belonging to any lattice band.
• An example of invisible defect is presented for a PT-symmetric Mathieu crystal.

We show that invisible localized defects, i.e. defects that cannot be detected by an outside observer, can be realized in a crystal with an engineered imaginary potential at the defect site. The invisible defects are synthesized by means of supersymmetric (Darboux) transformations of an ordinary crystal using band-edge wavefunctions to construct the superpotential. The complex crystal has an entire real-valued energy spectrum and Bragg scattering is not influenced by the defects. An example of complex crystal synthesis is presented for the Mathieu potential.